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Among the iron-based pnictide superconductors the material KFeAs is unusual in that its Fermi surface does not consist of quasi-nested electron and hole pockets. Here we report measurements of the temperature dependent London penetration depth of very clean crystals of this compound with residual resistivity ratio . We show that the superfluid density at low temperatures exhibits a strong linear-in-temperature dependence which implies that there are line nodes in the energy gap on the large zone-centered hole sheets. The results indicate that KFeAs is an unconventional superconductor with strong electron correlations.

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